270 



THEORY OF SEAKEEPING 



200 



; 150 

 > 



; 100 



: 50 

 



Si 



-'40 



-o 



o 



J 30 



C 



0) 



E 20 



o 



s; 



Dl 



c 10 



Conven+ional Static 



Cotcula+ion- Sag~^ 

 Con ventional Static Calcu lation -j w'ith Smith Ettect Soq^^* 



dift'erent dynamometers, were published by E. V. Lewis 

 (1958). These data are shown in Fig. 20. The com- 

 pari.son of Jacob's (1958) computed bending moments 

 witli new experimental data is summarized as follows: 



Modfl 



speed, 



fps 







2.4 



Calculated 



23 

 21 



Experimental 

 20 



0) -! 



5 20 

 



oLf^o 



"5 — r 



Average Total Amplitude of Heave 

 andPi^ch, Upand Down 



Followtng Seas 

 Pitch , 



- 2 

 



40 



oi 



10 0-20 



c" 



Average Total Amplitude ot Vertical 

 Motions at Ends, Up and Down 



Average Peak Vertical 

 Accelerations ot Ends 



Following Seas 



f-S^T"! Head Seas 



;5 20 1,5 1,0 06 0.5 1.0 

 Model Speed- Knots 



1.5 2,0 2,5 



25 20 IE 10 5 5 10 15 20 25 

 Ship Speed-Knots 



Fig. 14 Effect of speed on bending moments and motions, 



model of T2-SE-A1 tanker in regular L 20 waves (from E. V. 



Lewis, 1954) 



two model speeds, and 2 fps. The computational 

 points are indicated by crosses. 



Bending moments for a restrained model in waves of 

 /( = X 20 are shown in Fig. 19. In this case there is no 

 model motion and no acceleration force. The diagram 

 shows, therefore, directly the degree of agreement in the 

 calculation of hydrodynamic forces. These data can 

 be summarized as follows: 



Model 



speed, 



fps 







9 



Total range of bending 

 — moment, in-lb- 



Calculated 



101 

 100 



Experimental 

 89 

 88 



The original test data for a free model in waves 

 of h = X, 20 were shown in Fig. 16 for comparison with 

 tests in irregular waves. As this was already stated, the 

 dip of the bending-moment curve at synchronous speed 

 was later traced to an instrumental error. The results 

 of repeated tests in less steep waves {h = X/48), using 



The most important feature of Jacobs' (1958) analysis 

 is the subdi\-ision of the total bending moments into its 

 several components. This is shown in Fig. 21 for the 

 free model at 2.4 fps. The diagram corresponds to the 

 instant, t = 0, at which the wave crest is at the front 

 perpendicular. At this instant, the calculated and ex- 

 perimental .sagging bending moments are near their 

 maxima. In this analyzed case the waves were low, 

 and the Smith effect, shown by the dotted line, is rela- 

 tively small. The inertial effect of the added mass of 

 water (dash-double dot curve), however, is very strong 

 and is deducted from the displacement force. The 

 effect of the forces caused by water velocities (dash-dot 

 cur\-e) is also significant over the forebody and tends to 

 increase the bending moment. The final loading curve 

 is the result of summation of the hull inertia forces and 

 of foiu' components of water pressure forces. It is there- 

 fore very sensitive to the errors in computation of indi- 

 vidual components. The bending moment can be con- 

 sidered in fact as a "second-order effect" in that it is the 

 residt of a rdativelij ■•<mnll difference of large components. 



4.2 ' K. Oehi— A Cargo Ship. K. Ochi (1956a and b, 

 1957, 1958o) published the results of extensive towing- 

 tank tests of two cargo-ship models with U and V-bow 

 sections. The body plans of models \\ere shown in Fig. 

 2-25, and the particulars are given in Table 5. One of 

 the major objectives of tests was to obtain the informa- 

 tion on slamming. The discussions of this subject, how- 

 ever, will be deferred to later sections and only normal 

 bending moments now will be considered. 



Six-meter-long (19.7 ft) models were made of brass 

 and were tested in a 655-ft-long towing tank.^'^ All 

 runs were made in head seas under the self-propulsion 

 method and the models were free to pitch, heave and 

 surge. Moilel motions are shown in Figs. 22 and 23 and 

 phase relationships are shown in Fig. 24. These figures 

 refer to the wave length, X, equal to the ship's length, L, 

 and to the wa^e height of L/30. Bending stresses at 

 the deck amidships arc shown in Fig. 25 for different 

 values of the ship's draft, d. The draft ratio d/L = 

 0.059 corresponds to a fully loaded ship. Sagging 

 stresses are plotted as negative and hogging stresses as 

 positive. Ochi's data, shown in Fig. 25 are in agree- 

 ment with Lewis' Fig. 14 in that below .synchronous 

 speed the bending moment or stress is essentiallj' inde- 

 pendent of speed. Above synchronous speed there is a 

 gradual iiicrea.se of stress. 



"See Ochi (UI58«) for detailed description of the models, test 

 schedules, and results obtained. 



